For those that aren't familiar with this. Shamelessly taken from public documentation of projects.
Typical "before" pic in PA of a stream in need of legacy sediment removal: The brown dirt is accumulated agricultural runoff from years and years of agriculture, mill dams, and the like. You can see on the far bank near the stream, a blacker soil. That's the original soil, the brown soil is deposited on top. The stream cuts a narrow channel down through the brown stuff and gets to the original streambed, but you have unstable banks and lots of siltation in the streambed itself, all being carried downstream too.
And the intended outcome after a project. They take off all of the brown dirt from around the stream and get down to the original gravel/spongy black soil and plant grasses. They basically make a swampy area. As for thermal benefits, remember that this is a swamp with spongy soil. A lot of the water is actually underground.
Same spot during a high water event:
Instead of a fast runoff of chocolate milk, you have a slower, wider wetter swamp filtering through grasses and shrubs, reducing siltation that's carried downstream. And thermal benefits come from more groundwater interaction.
I have zero problem with that approach where it makes sense, mainly in lowland treeless farm areas like the first pic. This is not a high, forested country thing for sure. Lycoflyfisher is correct, not all streams were widely braided meadows. Many piedmont streams, like Hammer, are like this in the headwaters and proceed to flow through forests and hills downstream to take on a more classic trout stream look. Starting with colder, cleaner water with less silt is a good thing. The farmer loses some acreage is why it's tough to do. But yes, in a perfect world I'd plant some willows and wetland resistant trees in that swamp, no doubt. They'll take where they should, and die where they shouldn't.